Taking the Back

I always hear John Danaher saying if you can see the back, you can take the back. It is both that simple and incredibly difficult at the same time. Since part of the work is already done for us, let's leave turtle out of this discussion and focus on the types of back exposure that begin from head on positioning.
Opponent is supine:
When our opponent is on his back facing upwards, there are three ways I can think of that encompass the majority if not all of the ways to take the back. 
Force to one side or the other: this one is fairly simple, and can be a result of our opponent turning to their side to escape or of a conscious decision on our part to funnel them into a back take. Oftentimes, this is aided by the giftwrap head and arm control and a wedge with our shin to scoop them into the control position.
Shoulder exposure: there are two common ways that come to mind when I think about back takes where the shoulders are exposed to achieve the position. The classic stand 'em up sit 'em down from north south and the "vortex" position in both instances we take the back by lifting both shoulders from the ground first to set our hooks.
hip exposure- This is the back take that gets the cheers, utilized in positions like the truck, rolling back takes, or chained off the double under hook pass, elevating the hips from the ground and setting the hooks in is highlight reel worth stuff and proven to be competition effective.

What if we are on the bottom?
I've thought about 4 major ways that back takes from the bottom happen.
Chest to shoulder: It's classic, it works. We drag their arm across our body, pin their shoulder with our chest and begin setting the hooks in. Arm drags and off center closed guard attacks are great examples of the chest shoulder back exposure method.
Underhooks: Another classic, anytime you can achieve underhooks from a bottom position, you can threaten to take the back. 
Armpit to armpit: It almost seems like an accident, but there are whole instructionals about octopus guard and lots of footage of people getting their back taken by understanding back takes with an armpit to armpit connection.
Chair sit: A move for the cool kids, kiss of the dragon, matrix, deep 1/2 they all have a version of a chair sit back take. Once you've gotten mostly behind your opponent, connect somehow to their hips, exploit their balance using your shins, and sit them down to place the hooks.
A very simplified overview of back exposure options, if you have one that you feel doesn't fit within these parameters, I'll happily add it.